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Preparing for Assessment
73.
What is the value of
f
[
g
(5)] if
f
(
x
)
=
x
+
2
_
2
and
g
(
x
)
=
x
2
−
2?
1
A
3
1
_
2
B
10
1
_
4
C
12
1
_
2
D
23
74.
Let
f
(
x
)
=
x
2
+
1. What is the value of
f
(
f
(3))?
1
A
2
B
10
C
82
D
101
75.
For which pair(s) of functions is [
f
◦
g
](
x
) a
quadratic function?
7
A
f
(
x
)
=
x
2
and
g
(
x
)
=
3
x
+
7
B
f
(
x
)
=
x
−
4 and
g
(
x
)
=
x
2
−
1
C
f
(
x
)
=
x
+
9 and
g
(
x
)
=
2
x
−
3
D
f(x)
=
x
and
g
(
x
)
=
6
x
E
f(x)
=
x
2
−
1 and
g
(
x
)
=
x
2
+
1
F
f(x)
=
x
2
−
4
and
g
(
x
)
=
3
x
76.
If
f
(
x
)
=
2
x
+
1 and
g
(
x
)
=
4
x
−
5, which of the
following is [
f
◦
g
](
x
)?
1
A
[
f
◦
g
](
x
)
=
8
x
−
9
B
[
f
◦
g
](
x
)
=
8
x
−
4
C
[
f
◦
g
](
x
)
=
8
x
−
1
D
[
f
◦
g
](
x
)
=
8
x
−
10
77.
Find (
f
◦
g
)(4) for the following functions.
1, 6
f
(
x
)
=
2
x
+
5
g
(
x
)
=
x
2
-
2
x
+
3
78.
Find (
g
◦
f
)(
-
2) for the following functions.
1, 6
f
(
x
)
= -
x
2
+
6
x
-
1
g
(
x
)
=
2
x
2
-
3
x
A
−
113
C
629
B
476
D
1084
79.
The graphs of
f
(
x
) and
g
(
x
)
are shown.
What is [
f
◦
g
](2)?
7
A
−
8
B
−
3
C
2
D
4
80.
If
f
(
x
)
=
x
2
−
8 and
g
(
x
)
=
3
x
+
1, what is the value
of [
g
◦
f
](
−
4)?
6
[
g
◦
f
](
−
4)
=
81.
MULTI-STEP
Amelia is shopping at an online
store. Shipping for each order costs a flat fee of
$6.75. Sales tax is 8%.
1, 4
a.
Let
x
represent the cost of an order before
shipping or sales tax. Write a function
s
(
x
) that
represents the cost of an order with shipping,
and a function
t
(
x
) that represents the cost of
an order with sales tax.
b.
Find [
s
◦
t
](
x
) and explain what this function
represents.
c.
Find [
t
◦
s
](
x
) and explain what this function
represents.
d.
Will Amelia get a better deal if the shipping fee
is applied to the order before sales tax, or after
sales tax? Explain.
C05_038A_903990
y
x
O
f
(
x
)
g
(
x
)
328
|
Lesson 5-2
|
Composition of Functions